PRODUCT STRUCTURES AND FRACTIONAL INTEGRATION ALONG CURVES IN THE SPACE

被引：0
|
作者：
Casarino, Valentina [1 ]
Ciatti, Paolo [2 ]
Secco, Silvia [2 ]
机构：
[1] Univ Padua, DTG, I-36100 Vicenza, Italy
[2] Univ Padua, DICEA, I-35131 Padua, Italy
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2013年 / 6卷 / 03期
关键词：
Product kernels; fractional integration along curves in the space; strong L-p bounds; SINGULAR-INTEGRALS; ANALYTIC FAMILIES; KERNELS;
D O I：
10.3934/dcdss.2013.6.619
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we establish L-p boundedness (1 < p < infinity) for a double analytic family of fractional integrals S-z(gamma), gamma, z is an element of C, when Rez = 0. Our proof is based on product-type kernels arguments. More precisely, we prove that the convolution kernel of S-z(gamma) is a product kernel on R-3, adapted to the polynomial curve x1 bar right arrow (x(1)(m), x(1)(n)) (here m, n is an element of N, m >= 1, n > m).
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页码：619 / 635
页数：17
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